I can understand what you are experiencing because I used to have the exact same problem. It took some time to overcome the issue and I tried several things before discovering what works really well for me.
While there is no doubt that an ultra thin pick will make it impossible to play as loudly as you can with a thicker pick, the feel of a thin pick is dramatically different and you lose some control because of the bending and delayed springback.
The volume is determined by how forcefully you deflect the string with your pick. To prove this pluck any open string with barely enough lateral deflection to cause the string to vibrate and make a sound. Now deflect the same string a farther distance. You will notice the farther you deflect the string before letting it go to vibrate, the louder the sound.
You can lightly deflect the string with a heavy pick. There is a limit to how much you can deflect a string with an ultra thin pick that will itself deflect - this preventing maximum string deflection. But as I said, I prefer the greater control of a stiffer pick.
The trick is to learn to strum lighter by brushing the pick lightly across the strings rather than digging in. Even with a tight grip on your pick, you are more likely to drop your pick if you dig the pick too deep into the strings because the pushback from the strings will be greater as you place more of the meat of the pick against the strings. The string will act like a slingshot and shoot your pick right out of your hand (used to happen to me often).
It just take practice to develop a lighter strumming hand technique where you are able to control how much your pick digs into the strings. To play more quietly (even with a heavy pick), you want to barely brush the strings with just the tip of your pick.
You also will get less deflection if you angle the pick as it brushes across the string. To prove this - barely hold the fat end of your pick between your fingers very loosely and brush the pick across the strings allowing it to be almost parallel to the fretboard and see how much less volume you get than if you strum with the pick at a 90 degree angle to the strings.
I have tried holding the pick with less of it exposed to sort of force myself to play with just the tip, but I personally found that counter productive.
The technique I use to strum with less volume is to hold the pick in a manner that allows it to flex back and forth like a paint brush on a wall. If you paint a flat surface with a paint brush, you want the brush to bend one way when you brush up and the opposite way when you brush down. Same thing with your pick. You don't want the pick at a 90 degree angle to your strings or it becomes far more difficult to execute that light brush effect that I refer to.
If you grip the pick so that only the tip is exposed, you won't be able to allow the pick to flex back and forth as you brush it across the strings.
Another thing you can do to reduce the deflection and volume on your downstrums is to angle the pick slightly so that it is slicing through the strings as if your pick was a knife blade and you were going to cut the strings. This will alter the tone but reduce the volume.
Finally, in many songs, palm muting is very effective. Palm muting (like developing a lighter strumming technique) is another technique that take a great deal of time and practice to perfect. But once you master it, it becomes second nature and you will start finding more situations where it is effective in creating not only less volume, but more of a rhythmic feel to your strumming.
The bottom line is that you just need to consciously practice a lighter strum using less bite of the pick so that string deflection is reduced. Eventually it will come naturally and you will be able to control the volume as needed.
Good luck and have fun with your music!